Correlation Functions in ω\omega-Deformed N=6 Supergravity

Gauged N=8 supergravity in four dimensions is now known to admit a deformation characterized by a real parameter $\omega$ lying in the interval $0\le\omega\le \pi/8$. We analyse the fluctuations about its anti-de Sitter vacuum, and show that the full N=8 supersymmetry can be maintained by the boundary conditions only for $\omega=0$. For non-vanishing $\omega$, and requiring that there be no propagating spin s>1 fields on the boundary, we show that N=3 is the maximum degree of supersymmetry that can be preserved by the boundary conditions. We then construct in detail the consistent truncation of the N=8 theory to give $\omega$-deformed SO(6) gauged N=6 supergravity, again with $\omega$ in the range $0\le\omega\le \pi/8$. We show that this theory admits fully N=6 supersymmetry-preserving boundary conditions not only for $\omega=0$, but also for $\omega=\pi/8$. These two theories are related by a U(1) electric-magnetic duality. We observe that the only three-point functions that depend on $\omega$ involve the coupling of an SO(6) gauge field with the U(1) gauge field and a scalar or pseudo-scalar field. We compute these correlation functions and compare them with those of the undeformed N=6 theory. We find that the correlation functions in the $\omega=\pi/8$ theory holographically correspond to amplitudes in the U(N)_k x U(N)_{-k} ABJM model in which the U(1) Noether current is replaced by a dynamical U(1) gauge field. We also show that the $\omega$-deformed N=6 gauged supergravities can be obtained via consistent reductions from the eleven-dimensional or ten-dimensional type IIA supergravities.Comment: 38 pages, one figur

FRW and domain walls in higher spin gravity

We present exact solutions to Vasiliev's bosonic higher spin gravity equations in four dimensions with positive and negative cosmological constant that admit an interpretation in terms of domain walls, quasi-instantons and Friedman-Robertson-Walker (FRW) backgrounds. Their isometry algebras are infinite dimensional higher-spin extensions of spacetime isometries generated by six Killing vectors. The solutions presented are obtained by using a method of holomorphic factorization in noncommutative twistor space and gauge functions. In interpreting the solutions in terms of Fronsdal-type fields in spacetime, a field-dependent higher spin transformation is required, which is implemented at leading order. To this order, the scalar field solves Klein-Gordon equation with conformal mass in (anti) de Sitter space. We interpret the FRW solution with de Sitter asymptotics in the context of inflationary cosmology and we expect that the domain wall and FRW solutions are associated with spontaneously broken scaling symmetries in their holographic description. We observe that the factorization method provides a convenient framework for setting up a perturbation theory around the exact solutions, and we propose that the nonlinear completion of particle excitations over FRW and domain wall solutions requires black hole-like states.Comment: 63 page

Conformally invariant supersymmetric field theories on Sp × S1 and super p-branes

We construct supersymmetric field theories on Sp × S1 for p = 1,…,5. These spaces are the boundaries of the anti-de Sitter space in (p + 2)-dimensions. Thesetheories are invariant under the super extension of the anti-de Sitter group in (p + 2)-dimensions, whose bosonic subalgebra is SO(p + 1,2) asterisk in circle SO(N), for N = 1,2,4,8. The anti-de Sitter group SO(p + 1,2) acts as the conformal group on Sp × S1. We conjecture that these theories describe the super p-branes propagating in AdSp + 2 × SN−1. The internal space is always one of the parallelizable spheres, namely S1, S3 or S7

A note on positive energy of topologically massive gravity

I review how "classical SUGRA" embeddability establishes positive energy E for D=3 topologically massive gravity (TMG), with or without a cosmological term, a procedure familiar from D=4 Einstein gravity (GR). It also provides explicit expressions for E. In contrast to GR, E is not manifestly positive, due to the peculiar two-term nature of TMG.Comment: 7 page

An action principle for Vasiliev's four-dimensional higher-spin gravity

We provide Vasiliev's fully nonlinear equations of motion for bosonic gauge fields in four spacetime dimensions with an action principle. We first extend Vasiliev's original system with differential forms in degrees higher than one. We then derive the resulting duality-extended equations of motion from a variational principle based on a generalized Hamiltonian sigma-model action. The generalized Hamiltonian contains two types of interaction freedoms: One set of functions that appears in the Q-structure of the generalized curvatures of the odd forms in the duality-extended system; and another set depending on the Lagrange multipliers, encoding a generalized Poisson structure, i.e. a set of polyvector fields of ranks two or higher in target space. We find that at least one of the two sets of interaction-freedom functions must be linear in order to ensure gauge invariance. We discuss consistent truncations to the minimal Type A and B models (with only even spins), spectral flows on-shell and provide boundary conditions on fields and gauge parameters that are compatible with the variational principle and that make the duality-extended system equivalent, on shell, to Vasiliev's original system.Comment: 37 pages. References added, corrected typo

Kundt spacetimes as solutions of topologically massive gravity

We obtain new solutions of topologically massive gravity. We find the general Kundt solutions, which in three dimensions are spacetimes admitting an expansion-free null geodesic congruence. The solutions are generically of algebraic type II, but special cases are types III, N or D. Those of type D are the known spacelike-squashed AdS_3 solutions, and of type N are the known AdS pp-waves or new solutions. Those of types II and III are the first known solutions of these algebraic types. We present explicitly the Kundt solutions that are CSI spacetimes, for which all scalar polynomial curvature invariants are constant, whereas for the general case we reduce the field equations to a series of ordinary differential equations. The CSI solutions of types II and III are deformations of spacelike-squashed AdS_3 and the round AdS_3, respectively.Comment: 30 pages. This material has come from splitting v1 of arXiv:0906.3559 into 2 separate papers. v2: minor changes

BRST-antifield-treatment of metric-affine gravity

The metric-affine gauge theory of gravity provides a broad framework in which gauge theories of gravity can be formulated. In this article we fit metric-affine gravity into the covariant BRST--antifield formalism in order to obtain gauge fixed quantum actions. As an example the gauge fixing of a general two-dimensional model of metric-affine gravity is worked out explicitly. The result is shown to contain the gauge fixed action of the bosonic string in conformal gauge as a special case.Comment: 19 pages LATEX, to appear in Phys. Rev.

Massive higher spins and holography

We review recent progress towards the understanding of higher spin gauge symmetry breaking in AdS space from a holographic vantage point. According to the AdS/CFT correspondence, N=4 SYM theory at vanishing coupling constant should be dual to a theory in AdS which exhibits higher spin gauge symmetry enhancement. When the SYM coupling is non-zero, all but a handful of HS currents are violated by anomalies, and correspondingly local higher spin symmetry in the bulk gets spontaneously broken. In agreement with previous results and holographic expectations, we find that, barring one notable exception (spin 1 eating spin 0), the Goldstone modes responsible for HS symmetry breaking in AdS have non-vanishing mass even in the limit in which the gauge symmetry is restored. We show that spontaneous breaking a' la Stueckelberg implies that the mass of the relevant spin s'=s-1 Goldstone field is exactly the one predicted by the correspondence.Comment: 8 pages, talk presented by M.B. at the "Fourth Meeting on Constrained Dynamics and Quantum gravity" held in Cala Gonone (Sardinia, Italy), September 12-16, 200

Variant N=(1,1) Supergravity and (Minkowski)_4 x S^2 Vacua

We construct the fermionic sector and supersymmetry transformation rules of a variant N=(1,1) supergravity theory obtained by generalized Kaluza-Klein reduction from seven dimensions. We show that this model admits both (Minkowski)_4 x S^2 and (Minkowski)_3 x S^3 vacua. We perform a consistent Kaluza-Klein reduction on S^2 and obtain D=4, N=2 supergravity coupled to a vector multiplet, which can be consistently truncated to give rise to D=4, N=1 supergravity with a chiral multiplet.Comment: Latex, 17 pages. Version appearing in Classical and Quantum Gravit

(2,0) Chern-Simons Supergravity Plus Matter Near the Boundary of AdS_3

We examine the boundary behaviour of the gauged N=(2,0) supergravity in D=3 coupled to an arbitrary number of scalar supermultiplets which parametrize a Kahler manifold. In addition to the gravitational coupling constant, the model depends on two parameters, namely the cosmological constant and the size of the Kahler manifold. It is shown that regular and irregular boundary conditions can be imposed on the matter fields depending on the size of the sigma model manifold. It is also shown that the super AdS transformations in the bulk produce the transformations of the N=(2,0) conformal supergravity and scalar multiplets on the boundary, containing fields with nonvanishing Weyl weights determined by the ratio of the sigma model and the gravitational coupling constants. Various types of (2,0) superconformal multiplets are found on the boundary and in one case the superconformal symmetry is shown to be realized in an unconventional way.Comment: 28 pages, latex, references adde